I don't agree with the parent on may of their claims, but I want to ask about a few of yours.
More than half of teachers identify as Republicans or Independents (https://www.edweek.org/leadership/survey-educators-political-leanings-who-they-voted-for-where-they-stand-on-key-issues/2017/12). 40% of teachers identified as Democrats.
You can't lump Republicans and Independents together because many independents lean Democrat. The parent poster specifically commented on Republican teachers which make up less than 35% and may be around 27%. You only get to 35% if you include independents that "lean right". The parent is still wrong, but your numbers misrepresent republican views in education too.
https://www.pewresearch.org/social-trends/2024/04/04/teachers-views-on-the-state-of-public-k-12-education/
And if money doesn't matter in education, then why do rich families send their children to schools that spend more per student than poor families? Do rich people love throwing away money on education if it really makes no difference?
It really comes down to per-pupil education costs. Private schools have a higher per-pupil in the classroom cost and lower admin costs. That is just the nature of government vs private entities. Private entities tend to have leaner administrative structure. Spending per pupil is a very good metric if you compare apples-to-apples. So you are correct, it needs to be looked at district by district. Do you really think parents would spend massive amounts on private education if the administrative costs were high and spending per-pupil was low? Obviously not. For example, at the private school we send out grand-child. The classroom size is capped at 15. At our public school (in a very wealthy area), classrooms can reach 30 students. Which model do you think spends more per-pupil? Which model do you think give more individualized attention per student.
The other benefit to private schools are they tend to push students to the high end vs teach to the average. If the students can't cut it, they can always attend public school. Public schools don't have that option. Thus, and this is a hard truth, there are students that slow down the pace of the class. Teachers have to differentiate their strategies per student (or so we are told). What they do is differentiate to raise the low-performance students to just below average, and then lower the overall average performance of the other students so it aligns. Why? Because if you don't help a struggling kid out, you get in a lot of trouble. If you fail to differentiate for an excelling student, you don't get in trouble. Simple as that. Not to mention many school districts are doing away with "gifted and talented" - stupid way to name it - eliminating advanced classes.